For starting the studies in Mathematical-Biology I will take an undergraduate course in Mathematical Biologylearn themes like: 
population dynamics; the emergence of patterns of Philotaxia; Turing´s bifurcation; Genetics; Chaos; Neural networks; etc...
What books do you know/recommend for the study of these topics?
(I have taken calculus (one and many variables) and a course on ODE´s, but have no knowledge of PDE´s. I have knowledge of analysis, algebra and topology, too).
 A: First of all, I would recommend taking a course. You can find one at many universities in Canada where I am. It is unlikely they will cover all of these topics though. Here are some references. 
population dynamics: 
Otto and Day http://press.princeton.edu/titles/8458.html
Linda Allan https://www.amazon.ca/Introduction-Mathematical-Biology-Linda-Allen/dp/0130352160 these are two popular texts and have a lot of the basics in them. 
the emergence of patterns of Philotaxia; 
If you mean Fibonacci numbers/ patterns, here is a neat web page: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html
If you want some more hard core math on pattern formations (shell patterns), check our Murry:http://www.ift.unesp.br/users/mmenezes/mathbio.pdf
Turing´s bifurcation; 
Most Mathbio books have sections on bifurcations (see Otto Day and Linda Alan and others)
note: http://www.math.pitt.edu/~bard/xpp/whatis.html
I used this software at workshop/school. Made generating bifurcation plots super easy.  
Genetics; 
New more info on what you want. In Otto and Day you will see how to study evolution through modelling. this book explains why certain traits (which are determined by genes) are seen in nature (mathematically). or maybe something from Martin Nowak: https://books.google.ca/books?id=YXrIRDuAbE0C&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false 
To study evolution is to study genes.. in a way.. 
Chaos; 
Maybe Murray again http://www.ift.unesp.br/users/mmenezes/mathbio.pdf
I think there is a section on Logistic growth and chaos. this can be found in a dynamical systems text as well, like Clark Robinson https://www.amazon.ca/Dynamical-Systems-Stability-Symbolic-Dynamics/dp/0849384958
Neural networks;
I took this course back in 2010 https://www.pims.math.ca/scientific-event/100510-mbn and it was fantastic! I see one of the Profs has a book in the works:
http://www.springer.com/us/book/9780387877075
